Higgs to invisible at the FCC-ee

The expected sensitivity, using statistical errors only, to the branching fraction of Higgs to invisible is given for the $ZH$ process at the $e^+e^-$ Future Circular Collider running at  centre-of-mass energies of $\sqrt{s}=240$~GeV and $\sqrt{s}=365$~GeV with integrated luminosities of 10.8~ab$^{-1}$ and 3~ab$^{-1}$ respectively. The decays of the $Z$ to electrons, muons, $b$-quarks, $c$-quarks and lighter quarks were investigated. It is found that a  25\% measurement is possible if a Standard Model branching fraction of 0.106\%  for the process $H\to ZZ^* \to \nu\nu\nu\nu$ is assumed. The $Z\to qq$ channel has the best sensitivity. Additional new physics Higgs to invisible decays could be observed with a sensitivity of greater than $5\sigma$ if the branching fraction exceeds 0.13\% or could be excluded at 0.052\% at  95\% confidence level.